Answer
The solutions are $x=12$ and $x=2$.
Work Step by Step
The given equation is
$\Rightarrow |2x+1|=|3x-11|$
Write related linear equations.
$\Rightarrow 2x+1=3x-11$ or $2x+1=-(3x-11)$
Solve the first equation.
$\Rightarrow 2x+1=3x-11$
Add $11-2x$ to each side.
$\Rightarrow 2x+1+11-2x=3x-11+11-2x$
Simplify.
$\Rightarrow 12=x$
Solve the second equation.
$\Rightarrow 2x+1=-(3x-11)$
Use distributive property.
$\Rightarrow 2x+1=-3x+11$
Add $3x-1$ to each side.
$\Rightarrow 2x+1+3x-1=-3x+11+3x-1$
Simplify.
$\Rightarrow 5x=10$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=\frac{10}{5}$
Simplify.
$\Rightarrow x=2$
Check $x=12$
$\Rightarrow |2x+1|=|3x-11|$
$\Rightarrow |2(12)+1|=|3(12)-11|$
$\Rightarrow |24+1|=|36-11|$
$\Rightarrow |25|=|25|$
$\Rightarrow 25=25$
True.
Check $x=5$
$\Rightarrow |2x+1|=|3x-11|$
$\Rightarrow |2(2)+1|=|3(2)-11|$
$\Rightarrow |4+1|=|6-11|$
$\Rightarrow |5|=|-5|$
$\Rightarrow 5=5$
True.
Hence, the solutions are $x=12$ and $x=2$.
